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associatedCastelnuovoSurface -- Castelnuovo surface associated to a rational complete intersection of three quadrics in P^7

Synopsis

Description

More details will be provided in a forthcoming paper by F. Russo and G. Staglian├▓.

i1 : X = specialFourfold random({5:{1}},0_(PP_(ZZ/33331)^7));

o1 : ProjectiveVariety, complete intersection of three quadrics in PP^7 containing a surface of degree 1 and sectional genus 0
i2 : describe X

o2 = Complete intersection of 3 quadrics in PP^7
     of discriminant 31 = det| 8 1 |
                             | 1 4 |
     containing a surface of degree 1 and sectional genus 0
     cut out by 5 hypersurfaces of degree 1
     (This is a classical example of rational fourfold)
i3 : time U' = associatedCastelnuovoSurface X;
 -- used 5.93437s (cpu); 2.21093s (thread); 0s (gc)

o3 : ProjectiveVariety, Castelnuovo surface associated to X
i4 : (mu,U,C,f) = building U';
i5 : ? mu

o5 = multi-rational map consisting of one single rational map
     source variety: 5-dimensional subvariety of PP^7 cut out by 2 hypersurfaces of degree 2
     target variety: PP^4
     dominance: true

See also

Ways to use associatedCastelnuovoSurface :

For the programmer

The object associatedCastelnuovoSurface is a method function with options.